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The standard deviation of a certain set of data is 3. If 20 is 2 stand
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09 Jun 2022, 02:00
09 Jun 2022, 02:00
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The standard deviation of a certain set of data is 3. If 20 is 2 standard deviations away from the mean, which of the following values could be the mean of the set of data?
A. 14
B. 18
C. 20
D. 24
E. 25
A. 14
B. 18
C. 20
D. 24
E. 25
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
Re: The standard deviation of a certain set of data is 3. If 20 is 2 stand
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09 Jun 2022, 08:36
09 Jun 2022, 08:36
If the standard deviation is 3, two standard deviations is 6.
Thus, if 20 is two standard deviations away from the mean, it can either be 20-4=14 or 20+6=26
A
Thus, if 20 is two standard deviations away from the mean, it can either be 20-4=14 or 20+6=26
A
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Re: The standard deviation of a certain set of data is 3. If 20 is 2 stand
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09 Jun 2022, 09:38
09 Jun 2022, 09:38
1
Carcass wrote:
The standard deviation of a certain set of data is 3. If 20 is 2 standard deviations away from the mean, which of the following values could be the mean of the set of data?
A. 14
B. 18
C. 20
D. 24
E. 25
A. 14
B. 18
C. 20
D. 24
E. 25
----------------------ASIDE-----------------------------------------------------
A little extra background on standard deviations above and below the mean
If, for example, a set has a standard deviation of 4, then:
1 standard deviation = (1)(4) = 4
2 standard deviations = (2)(4) = 8
3 standard deviations = (3)(4) = 12
1.5 standard deviations = (1.5)(4) = 6
0.25 standard deviations = (0.25)(4) = 1
etc
So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean = 17 [since 9 + 2(4) = 17]
1.5 standard deviations BELOW the mean = 3 [since 9 - 1.5(4) = 3]
3 standard deviations ABOVE the mean = 21 [since 9 + 3(4) = 21]
etc.
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Given: 20 is 2 standard deviations away from the mean
So 20 is either two standard deviations ABOVE the mean or two standard deviations BELOW the mean.
If we let M = the mean, then there are two possibilities:
If 20 is two standard deviations BELOW the mean, then we can write: M - 2(3) = 20. When we solve this, we get M = 26, which isn't among the answer choices
If 20 is two standard deviations ABOVE the mean, then we can write: M + 2(3) = 20. When we solve this, we get M = 14, which means the answer is A
